Decrease in Computational Load and Increase in Accuracy for Filtering of Random Signals - Phil Howlett; Anatoli Torokhti; Pablo Soto-Quiros (Mathematics, 2025)
This paper describes methods for optimal filtering of random signals that involve large matrices. We developed a procedure that allows us to significantly decrease the computational load associated with numerically implementing the associated filter and increase its accuracy. The procedure is based on the reduction of a large covariance matrix to a collection of smaller matrices. This is done in such a way that the filter equation with large matrices is equivalently represented by a set of equations with smaller matrices. The filter we developed is represented by <semantics>x=<msubsup>∑j=1p</msubsup>Mjyj</semantics> and minimizes the associated error over all matrices <semantics>M1,…,Mp</semantics>. As a result, the proposed optimal filter has two degrees of freedom that increase its accuracy. They are associated, first, with the optimal determination of matrices <semantics>M1,…,Mp</semantics> and second, with an increase in the number p of components in the filter. The error analysis and results of numerical simulations are provided.